3 A marble block of mass mi 5510 kg and a granite block of mass m2 139.5 kg are
ID: 1883430 • Letter: 3
Question
3 A marble block of mass mi 5510 kg and a granite block of mass m2 139.5 kg are connected to each other by a rope that runs over a pulley as shown in the figure. Both blocks are located on inclined planes with angles 350° and ß- 56.8° The rope glides over the pulley without friction, but the coefficient of friction between block 1 and the inclined plane is H 0.13, and that between block 2 and the inclined plane is 2 0 31 (For simplicity, assume that the coefficients of static and kinetic friction are the same in each case) What is the acceleration of the marble block? Note that the positive r-direction is indicated in the figure? (1.66 m/s?)Explanation / Answer
here,
m1 = 551 kg
m2 = 139.5 kg
alpha = 35 degree
beta = 56.8 degree
u1 = 0.13
u2 = 0.31
the accelration of the system , a = net force /effective mass
a = (m1 * g * sin(alpha) - m2 * g * sin(beta) - friction force on m1 - friction force on m2) /( m1 + m2)
a = (m1 * g * sin(alpha) - m2 * g * sin(beta) - u1 * m1 * g * cos(alpha) - u2 * m2 * g * cos(beta)) /( m1 + m2)
a = ( 551 * 9.81 * sin(35) - 139.5 * 9.81 * sin(56.8) - 0.13 * 551 * 9.81 * cos(35) - 0.31 * 139.5 * 9.81 * cos(56.8) ) /( 551 + 139.5) m/s^2
a = 1.66 m/s^2
the accelration of the system is 1.66 m/s^2
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